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Physical Review A

Density-functional calculations in a two-dimensional finite-element basis for atoms in very strong magnetic fields: Energy values

Moritz Braun

Published Feb 27, 2002• 20 citations
Publisher

Abstract

Results of density-functional calculations for atoms in very strong magnetic fields using a two-dimensional finite-element basis set are reported for ground-state energies of helium, carbon, and neon, and for some excited states of helium. We give results obtained by using three different local-density functionals. A comparison with multi-Landau-channel Hartree-Fock calculations shows reasonable agreement for helium.

DOI
10.1103/physreva.65.033415

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Results of density-functional calculations for atoms in very strong magnetic fields using a two-dimensional finite-element basis set are reported for ground-state energies of helium, carbon, and neon, and for some excited states of helium. We give results obtained by using three different local-density functionals. A comparison with multi-Landau-channel Hartree-Fock calculations shows reasonable agreement for helium.
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The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.
Using a Hartree-Fock mesh method and a configuration-interaction approach based on a generalized Gaussian basis set, we investigate the behavior of the exchange and correlation energies of small atoms and molecules, namely, the helium and lithium atoms as well as the hydrogen molecule, in the presence of a magnetic field covering the regime B=0−−100a.u.B=0--100 \mathrm{a}.\mathrm{u}.B=0−−100a.u. In general, the importance of the exchange energy to the binding properties of atoms or molecules increases strongly with increasing field strength. This is due to the spin-flip transitions, and in particular due to the contributions of the tightly bound hydrogenic states which are involved in the corresponding ground states of different symmetries. In contrast to the exchange energy the correlation energy becomes less relevant with increasing field strength. This holds for the individual configurations constituting the ground state and for the crossovers of the global ground state.
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This is a mathematical study of certain aspects of the interacting electron system in very high perpendicular magnetic field.\nWe analyse restrictions imposed upon the density correlation functions of this system and propose a set of sum rules which they must obey.\nWe study the possibility of building a bosonisation scheme for the projected density operators in the lowest Landau level. We suggest a second order bosonisation, along with an approximation scheme, which may be useful for carrying out calculations in the lowest Landau level.\nWe analyse the possible ground states of the system. We suggest a set of variational wavefunctions which can have lower energy than the Laughlin state for sufficiently soft interaction potentials.\nWe study the collective excitations of the system, paying particular attention to its symmetries. We suggest a set of variational excited states and discuss their applicability to finite as well as infinite systems.